Numerical simulations of convective equilibrium under prescribed forcing

Some characteristic properties of simulated moist convective equilibria are examined for different imposed cooling rates. These numerical simulations extend the work of Vallis et al. and were motivated by the need to show that their conclusions (concerning the upscale energy cascade) were not sensitive to vertical resolution. Although kinetic energy does cascade to large scales, much of the large‐scale motion in the model is associated with horizontally‐divergent winds, and the energy spectra may be better explained as a direct consequence of the generation of convective lines. These lines have a typical spacing of about 60 km which leads to a local maximum in the kinetic‐energy spectrum. In addition, the design of our experiments was found to match that envisaged in recent idealized ‘heatengine theories’ of radiative‐convective equilibria, thereby providing an opportunity to evaluate their utility. It is shown that a variant of these scaling theories appears to fit the statistical properties of our simulations quite well and provides expressions for the convective available potential energy, cloud mass flux and the fractional area occupied by convective updraughts. Scaling arguments also suggest that the convective line separation is of the order of the convecting layer depth divided by the square root of the updraught fractional area—consistent with the wavelength of the local maximum in the energy spectrum.